Problem: $y=x^7$ $\dfrac{dy}{dx}=$
Answer: $y$ is of the form $x^n$ and therefore we can apply the power rule: $\dfrac{d}{dx}[x^n]=n\cdot x^{n-1}$ $\begin{aligned} \dfrac{dy}{dx}&=\dfrac{d}{dx}[x^{{7}}] \\\\ &={7}x^{{7}-1} \\\\ &=7x^6 \end{aligned}$ In conclusion, $\dfrac{dy}{dx}=7x^6$